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3 years ago

Solve the equation for all values of x by completing the square. 3x^2+177= -48x

Mathematics

1 answer:

GaryK [48]3 years ago

4 0

Use the formula

(

)

in order to create a new term. Solve for

by using this term to complete the square.

Exact Form:

√

−

Decimal Form:

−

5.76393202

…

−

10.23606797

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Barbara drives between Miami, Florida, and West Palm Beach, Florida. She drives 50 mi in clear weather and then encounters a thu

cluponka [151]

Answer:

Her speed driving in nice weather is 50 mph and in thunderstorm is 32 mph.

Step-by-step explanation:

Barbara drives 50 miles in clear weather and then encounters a thunderstorm for the last 16 miles.

Suppose, her speed in nice weather is $x$ mph.

As she drives 18 mph slower through the thunderstorm than she does in clear weather, so her speed in thunderstorm will be: $(x-18) mph$

We know that, $Time = \frac{Distance}{Speed}$

So, the time of driving in clear weather $=\frac{50}{x}$ hours

and the time of driving in thunderstorm $=\frac{16}{x-18}$ hours.

Given that, the total time for the trip is 1.5 hours. So, the equation will be......

$\frac{50}{x}+ \frac{16}{x-18}=1.5 \\ \\ \frac{50x-900+16x}{x(x-18)}=1.5\\ \\ \frac{66x-900}{x(x-18)}=1.5 \\ \\ 1.5x(x-18)=66x-900\\ \\ 1.5x^2-27x=66x-900\\ \\ 1.5x^2-93x+900=0\\ \\ 1.5(x^2 -62x+600)=0\\ \\ x^2 -62x+600=0\\ \\ (x-50)(x-12)=0$

Using zero-product property.........

$x-50=0\\ x=50\\ \\ and\\ \\ x-12=0\\ x=12$

We need to ignore $x=12$ here, otherwise the speed in thunderstorm will become negative.

So, her speed driving in nice weather is 50 mph and her speed driving in thunderstorm is (50-18) = 32 mph

3 0

3 years ago

I NEED ANSWERS TO THESE QUESTIONS

lisabon 2012 [21]

I only have the answer for 1, but !

1. The area of a parallelogram is base times height. Since the area of that rectangle is twice the area of the circle, then the area of the circle is half the base times the height. It will be half of 2πr· r. The area of the circle will be πr2

5 0

2 years ago

The variable Z is directly proportional to X. When X is 10, Z has the value 190.

irina [24]

Since z is proportion to the x
z = a x
190 = a 10
a = 19

when x = 13
z = a x
z = 19 * 13
z = 247

7 0

4 years ago

There are 250,000 cows in the barn 24,000 cows. went missing how many cows are in the barn

inessss [21]

226,000

Step-by-step explanation:

250,000-24,000=226,000

8 0

3 years ago

Read 2 more answers

Help!

Olin [163]

Answer:

2/16

1/8

Step-by-step explanation:

8/1=8

2/16=0.125 which is equal to 1/8

2/14=1/7

1/8=1/8 is 2/16 simplified so they are the same

14/2=7

6 0

3 years ago